HYDROLOGY 1

Introduction

• Water is abundant on Earth and is a key factor in air conditioning the planet for human existence.

• Hydrology is the study of all phases of the Earth's water.

Hydrologic Cycle

• The world's total volume of water exists in different forms:

  • Liquid: oceans, rivers, and rain

  • Solid: glaciers

  • Gas: invisible water vapor in the air

• Water changes states as it moves around the planet.

• Changes in distribution, circulation, or temperature can have far-reaching effects and may be caused by human activities.

  • hydrologic cycle

    

Branches of Hydrology

• Ecohydrology

• Hydrogeology

• Hydroinformatics

• Hydrometeorology

• Surface hydrology

• Drainage basin

• Water quality

• Chemical Hydrology

• Isotope hydrology

Application of Hydrology

• Design and operations of hydraulic structures

• Water supply

• Wastewater treatment and disposal

• Irrigation

• Drainage

• Navigation

• Erosion and sediment control

• Salinity control

• Pollution abatement

• Recreational use of water

• Fish and wildlife protection

• Hydropower generation

• Flood control

Hydrologic Budget

• Hydrologic budget, water budget, or water balance: A measurement of the continuity of water flow.

Applies to any time interval and area size.

Groundwater system hydrologic budget

ΔSg = I + G_in - G_out - Q_g - E_g - T_g

• Where:

  • G_in = groundwater flow into the system

  • G_out = groundwater flow out of the system

  • Q_g = groundwater flow into the stream

  • E_g = evaporation

  • T_g = transpiration

  • I = infiltration

  • $\Delta S_g$ = change in groundwater storage

• E_g and T_g can be significant if the water table is near the ground surface.

Surface water system hydrologic budget

ΔSs = P + Q_in - Q_out + Q_g - E_s - T_s - I

• Where:

  • P = precipitation

  • Q_in = surface water flow into the system

  • Q_out = surface water flow out of the system

  • Q_g = groundwater flow into the stream

  • E_s = surface evaporation

  • T_s= transpiration

  • I = infiltration

  • ΔSs = change in water storage of the surface water system

System hydrologic budget:

Δ(Ss + Sg) = P + Q_in - Q_out + G_in - G_out - E_s - E_g - T_s - T_g

• Simplified form:

  ΔS = P - Q - G - E - T

Water Quantities

• Estimated world water quantities:

  

Global Annual Water Balance

Residence Time

• The residence time ($T_r$) is the average duration of a water molecule to pass through a subsystem of the hydrologic cycle.

  $T_r = \frac{S}{Q}$

• S = volume of water

• Q = Flow rate

Precipitation

• Forces acting on a water droplet or ice crystal in a cloud:

  • Winds

  • Atmospheric stability

  • Gravity

  • Drag (friction)

• When a droplet reaches a critical mass, gravity exceeds other forces, causing precipitation.

• Raindrops are 100 times larger than cloud droplets.

Formation of Precipitation

1. Condensation and deposition:

   • If the rate of condensation exceeds evaporation, water accumulates on condensation nuclei.

   • Droplets grow slowly and rarely produce rain drops.

2. Collision and coalescence:

   • Larger droplets fall faster and collide with smaller ones.

   • If droplets coalesce, a larger drop forms.

   • If it gets big enough rain will fall

   • A drop must be larger to be an efficient collider.

   • If the drop is too big it will be less efficient, because it creates high pressure that pushes small drops out of the way

3. The Bergeron process:

   • Vapor pressure over ice is less than vapor pressure over water at the same temperature.

   • Water molecules move from water to ice and freeze on the ice.

   • If crystals grow large enough, they fall.

   • If they fall through cold air, it snows; if through warm air, it rains.

Growth of Ice Crystals

• Riming - super cooled water freezes onto ice crystals

• Aggregation - Ice crystals join together to form large snow flakes. Happens more readily if ice crystals have a thin coating of liquid

Types of Precipitation

• Rain

• Graupel

• Sleet

• Hail

• Freezing Rain

• Snow - Ice crystals grow in a cloud. Variety of shapes depending on temperature

Terminal Velocity

$V_{t}=\sqrt{\frac{4gD}{3C_{d}}\left(\frac{\rho_{w}}{\rho_{a}}-1\right)}$

• V = Terminal velocity

• g = gravity

• D = Diameter of droplet

• C = Drag coefficient

• ρ_w= Density of water (typically 1000 kg/m³ at 4°C)

• ρ_a = Denisty of air (approximately 1.225 kg/m³ at sea level and at 15°C)

  /s$</p></li></ul><h4 id="88d98ffd-5884-4e8f-80b3-51c0821b95c3" data-toc-id="88d98ffd-5884-4e8f-80b3-51c0821b95c3" collapsed="false" seolevelmigrated="true">Measurement of Precipitation</h4><ul><li><p>Standard rain gauges</p></li><li><p>Automated rain gauges</p></li><li><p>Tipping bucket rain gauge</p></li><li><p>Measuring Precipitation with Weather Radar</p></li><li><p>Measuring Precipitation Using Weather Satellites</p></li></ul><p><strong>Disdrometer</strong>: measures drop size distribution and velocity; distinguishes rain, graupel, and hail.</p><h3 id="9575332e-c0b0-4921-a611-0f719a902721" data-toc-id="9575332e-c0b0-4921-a611-0f719a902721" collapsed="false" seolevelmigrated="true">Rainfall Depth and Intensity</h3><ul><li><p>Determine the maximum depth and intensity for 5-min and 30-min rainfall interval</p></li><li><p>Max Intensity</p><p style="text-align: center">$I_{\max}=\frac{D_{\max}}{t}
  }}{5 \text{ min}} \times \frac{60 \text{ min}}{hr} = 7.92 \text{ in/hr}

• Cumulative rainfall calculation:

  • Cumulative @ 5 min = cum@0+ rainfall @5

  • Cumulative @ 10 min = cum@5+ rainfall @10

  • Cumulative @ 15 min = cum@10+ rainfall @15

  • Cumulative @ 20 min = cum@15+ rainfall @20

• Determine the maximum depth and intensity for 5-min and 30-min rainfall interval

• Given- 30-min interval recordings of rainfall

  n}}{30 \text{ min}} \times \frac{60 \text{ min}}{hr} = 4.18 \text{ in/hr}$</p></li></ul><h4 id="6173069f-bbd2-411c-ba36-fb269c565838" data-toc-id="6173069f-bbd2-411c-ba36-fb269c565838" collapsed="false" seolevelmigrated="true">Areal Rainfall</h4><ul><li><p>Averaging or Arithmetic Mean Method</p><ul><li><p>Simplest method.</p></li><li><p>Average rainfall depths recorded at gages.</p></li><li><p>$\text{Average rainfall} = \frac{\sum P_i}{n}$</p></li></ul></li></ul><h4 id="935170e0-b810-440a-b8e7-7f81edf4a3e2" data-toc-id="935170e0-b810-440a-b8e7-7f81edf4a3e2" collapsed="false" seolevelmigrated="true">Thiessen Polygon Method</h4><ul><li><p>If some gages are more representative, assign relative weights.</p></li><li><p>Assumes rainfall at any point is the same as at the nearest gage.</p></li></ul><h4 id="92ba6108-4687-4776-a62a-eb021a6cffed" data-toc-id="92ba6108-4687-4776-a62a-eb021a6cffed" collapsed="false" seolevelmigrated="true">Isohyetal Method</h4><ul><li><p>Construct isohyets (lines of equal rainfall) using observed depths and interpolation.</p></li><li><p>Use computer programs for automated contouring with a dense network of raingages.</p></li><li><p>Reciprocal squared distance method</p></li></ul><h3 id="c6522bef-f415-400f-bc55-6567d7db4361" data-toc-id="c6522bef-f415-400f-bc55-6567d7db4361" collapsed="false" seolevelmigrated="true">Return Period</h3><ol><li><p>Determine number of years of data, n</p></li><li><p>Set rainfall duration for analysis (5 minutely, hourly, daily, etc.)</p></li><li><p>Find maximum depth for duration in each year</p></li><li><p>Rank the depths from highest to lowest for all years</p><ul><li><p>Greatest amount at top of list, rank = m = 1</p></li></ul></li><li><p>Compute return period:</p><ul><li><p>$T = \frac{n+1}{m}$</p></li><li><p>where:</p><ul><li><p>n = number of years of data</p></li><li><p>m = rank of data from highest (m=1) to lowest (m=n)</p></li></ul></li></ul></li><li><p>Corresponding probability:</p><ul><li><p>$P = \frac{1}{T}

• (e.g., for t = 100 year event, the probability = 0.01)

• The formation of precipitation requires the lifting of an air mass in the atmosphere so that it cools and some of its moisture condenses

Types of Precipitation Caused by Air Mass Lifting

• Cyclonic Precipitation

• Orographic Precipitation

• Convective Precipitation

Evaporation

• Water Vapor

  • Atmospheric water mostly exists as a gas, or vapor, but briefly and locally it becomes a liquid in rainfall and in water droplets in clouds, or it becomes a solid in snowfall, in hail and in ice crystals in clouds The amount of water vapor in the atmosphere is less than 1 part in 100 000 of all waters of the earth, but it plays a vital role in the hydrologic cycle

Dalton's law & Vapor Pressure

• Dalton's law of partial pressures states that the pressure exerted by a gas (its vapor pressure) is independent of the presence of other gases

  e = ρ_v R_v T

  • Where:

    • e = Vapor pressure

    • R_v = Gas constant of water vapor

    • T = Absolute Temperature in K

    • ρ_v = Density of water vapor

• partial pressure due to the dry air (p - e)

  p - e = ρ_d R_d T

  • Where:

    • e = Vapor pressure

    • p = total pressure expected bt the moist air

    • R_d = Gas constant for dry air (287 J/kg-K)

    • T = Absolute Temperature in K

    • ρ_d = Density of dry air

• Density of moised air

  ρ_a = ρ_d + ρ_v

  • ρ_{a =} Density of moised air

  • ρ_d = Density of dry air

  • ρ_v = Density of water vapor

Specific Humidity

• Specific Humidity is the mass of water vapor per unit mass of moist air

  q_v = 0.622 \frac{e}{p}$</p></li><li><p>Where:</p><ul><li><p>$R_a$= Gas constant for dry air (287 J/kg-K)</p></li><li><p>$\rho_a$= Density of dry air</p></li><li><p>$\rho$= Density of moist air</p></li></ul></li><li><p>The relationship between the gas constants for moist air and dry air given by;</p><p style="text-align: center">R_a = R_d (1+0.608 q_v)</p><p style="text-align: center">R_a = 287 (1+0.608 q_v)</p></li></ul><h4 id="4552911b-b37b-43eb-8040-34e7210c79c3" data-toc-id="4552911b-b37b-43eb-8040-34e7210c79c3" collapsed="false" seolevelmigrated="true">Saturated Vapor Pressure</h4><ul><li><p>For a given air temperature, there is a maximum moisture content the air can hold, and the corresponding vapor pressure is called saturation vapor pressure.</p><p style="text-align: center">$e_s = 611e^{\frac{17.277}{237.3+T}}$</p></li><li><p>Where:</p><ul><li><p>$e_s$= Saturated vapor pressure of water vapor over liquid water, (Pa = N/m2)</p></li><li><p>T = Temperature (degree C)</p></li></ul></li></ul><h4 id="7919c64b-a8e0-4099-9c7f-318e842e204b" data-toc-id="7919c64b-a8e0-4099-9c7f-318e842e204b" collapsed="false" seolevelmigrated="true">Relative Humidity</h4><ul><li><p>Relative humidity is the ratio of the actual vapor pressure to its saturation value at a given air temperature:</p><p style="text-align: center">$Rh = \frac{e}{es}

Dew Point Temperature

• The temperature at which air would just become saturated at a given specific humidity is its dew point temperature

  {237.3+T}} = 1819 \text{ Pa}

Terminologies

• Evaporation - process by which liquid water passes directly to the vapor phase

• Transpiration - process by which liquid water passes from liquid to vapor through plant metabolism

• Sublimation - process by which water passes directly from the solid phase to the vapor phase

• Vapor pressure - water vapor normally behaves as an ideal gas

• Partial pressure of water (vapor pressure) adds to partial pressures of the other gaseous constituents

• Water vapor is about 12% of total pressure

• Humidity - quantity of water vapor present in air (absolute, specific or a relative value)

• Specific Humidity - ratio of mass of water vapor in moist air to mass of air

• Dew point temperature - temperature at which air becomes saturated at a given specific humidity

Factors Influencing Evaporation

• Energy supply for vaporization (latent heat)

  • Solar radiation

• Transport of vapor away from evaporative surface

  • Wind velocity over surface

  • Specific humidity gradient above surface

  • Vegetated surfaces

• Supply of moisture to the surface

  • Evapotranspiration (ET)

    • Potential Evapotranspiration (PET) moisture supply is not limited

Evaporation from Pan

• National Weather Service Class A type

• Filled with water to within 2.5 inches of the top

• Installed on a wooden platform in a grassy location

• Evaporation rate is measured by manual readings or with an analog output evaporation gauge

Methods Estimating Evaporation

• $Er=\frac{Rn}{LvPw}$

• Where:

  • Rn = net radiation, W/m2

  • $l_v$ = latent heat of vaporization, kj/kg

  • $P_w$ =density of water, kg/m3

Aerodynamic Method

$Ea=B(e_{s}-e)$

• B is the vapor transfer coefficient with units of mm/day

  $B=\frac{0.102u_2}{[ln(\frac{z_2}{z_0})]^2}$

• where wzis the wind velocity (m/s) measured at height z2(cm) and zo is the roughness height (0.01-0.06 cm) of the water surface.

Combined Method

$E=\left(\frac{\Delta}{\Delta+\gamma}\right)Er+\left(\frac{\gamma}{\Delta+\gamma}\right)Ea$

• $E_a$ is the vapor transport term and Er is the aerodynamic term.

• γ the psychrometric constant (approximately 66.8 Pa/C)

• Δ is the gradient of the saturated vapor pressure curve

  $\Delta = \frac{4098}{(237.3+T_a)^2}$

Priestly Taylor Method

$E=1.3\left(\frac{\Delta}{\Delta+\gamma}\right)E$